Question

An entrepreneur offers services that can be modeled as an s-server Erlang loss (Erlang-B) system. Suppose the arrival rate is 4 customers per hour; the average service time is 1 hour; the entrepreneur earns $ 2.50 for each customer served; and the entrepreneur’s operating cost is $1.00 per server per hour (whether the server is busy or idle).

a) The optimal number of servers, from the entrepreneur's point of view is: ??

b) If the entrepreneur deploys the optimal number of servers, he/she should expect to make a profit of ??$ per hour:

c) the maximum number of servers beyond which it is unprofitable for the entrepreneur to remain in business is: ??

Answer 1

a) As given arrival rate is 4 customer per hour and average service time 1 hour so it require atleast 4×1/1hour = 4 servers always required to handle 4 customer in an hour but it not optimal. Entrepreneurs must have 5 servers because it possible that 1customer may take more than 1 hour so they have atleast 1 extra server to Handel customer. Answer is Optimal 5 but atleast 4.

b) As optimal no. Of servers is 5 and the operating cost per hour will be $1.00 per server ×5 = $5 and income generated per hour will be 4×$2.5= $10 so he / she should expect a profit of $5 per hour .Answer is $5

c) Maximum income that can be generated per hour is $10 ($2.5×4) so maximum no. Of servers will 10 because operating cost of 10 servers is $10 per hour is equal to per hour incone. Answer is 10 servers.